# Thread: trigonometry problems

1. ## trigonometry problems

there are three questions.

1.Given that cos Ѳ = (1/2) and 270° < Ѳ < 360° , without using a calculator find the value of
(cos Ѳ – sin Ѳ)/(tan Ѳ+ sin Ѳ). Leave your answer as single fraction. Remain the surds as surds if there are surds in your answer.

2.Given that cos A = (1/2) and that cos A and sin A have the same sign, find the value of sin (–A) and of tan A.

3.Given that tan A = –(5/12) and that tan A and cos A have opposite signs, find the value of cos A and of cos [(∏/2)–A].

2. Originally Posted by wintersoltice
there are three questions.

1.Given that cos Ѳ = (1/2) and 270° < Ѳ < 360° , without using a calculator find the value of
(cos Ѳ – sin Ѳ)/(tan Ѳ+ sin Ѳ). Leave your answer as single fraction. Remain the surds as surds if there are surds in your answer.
Maybe this'll help!

3. Originally Posted by wintersoltice
there are three questions.

1.Given that cos Ѳ = (1/2) and 270° < Ѳ < 360° , without using a calculator find the value of
(cos Ѳ – sin Ѳ)/(tan Ѳ+ sin Ѳ). Leave your answer as single fraction. Remain the surds as surds if there are surds in your answer.

2.Given that cos A = (1/2) and that cos A and sin A have the same sign, find the value of sin (–A) and of tan A.

3.Given that tan A = –(5/12) and that tan A and cos A have opposite signs, find the value of cos A and of cos [(∏/2)–A].
alternatively, recall some useful identities:

$\sin^2 x + \cos^2 x = 1$

$\tan x = \frac {\sin x}{\cos x}$

you know what quadrants these angles will be in, if not, see what masters and kalagota did. couple these identities with the ones kalagota gave for problems 2 and 3, and it is straight arithmetic from there.

4. 2.Given that cos A = (1/2) and that cos A and sin A have the same sign, find the value of sin (–A) and of tan A.

Sin and Cos are both positive in Quadrant I and both negative in Quadrant III.

So if Cos A = 1/2, then the angle must be a QI angle.